Calculation of energy-saving effect from the use of parallel active filters in a three-phase fourwire power supply system with increasing the averaging interval of the measured values

Abstract

he apparent power of the three-phase four-wire supply system was decomposed into quadratic components under conditions of symmetric sinusoidal phase voltages. It was shown that the power factor for this mode is a product of the shift and asymmetry coefficients, the values of which are determined through the parameters of the symmetrical components of phase voltages and linear currents. The general formulas for calculating of the energy-saving effect from the application of shunt active filters in three-phase four-wire power system for the averaging the load power both on the network period and at any time interval were obtained. It was shown that in a power supply system with a constant in time nonlinear load the gain in the power losses when using shunt active filters is inversely proportional to the square of the power factor determined at the mains voltage period. The improved control law for the shunt active filter of a three-phase four-wire power supply system was proposed, which is distinguished by the increasing of the measured quantities averaging interval. It is shown for the first time that under conditions of stable phase voltage with the increasing of the averaging interval up to the period of the symmetrical load change, the gain coefficient of the power losses increases in comparison with the averaging at the mains voltage period in accordance with the value called the irregular energy consumption coefficient. The values of the irregular energy consumption coefficient for typical curves of the active power changing were obtained. In the case of a rectangular changing of the active power curve, the irregular energy consumption coefficient is determined by two parameters: the growth rate and the duty cycle. Its maximum meaning reaches a value of 2 in the case where the maximum power level is twice the average and the minimum level is zero. For periodic curves of active power, which are approximated by piecewise sinusoidal and piecewise linear dependencies, the irregular energy consumption coefficient is determined by one growth coefficient only regardless of the value of the duty cycle, reaching the maximum values of 3/2 and 4/3, respectively.Ref. 10, Fig. 2.